Cook the pasta according to package directions, adding the corn during the last 2 minutes of cooking. Reserve 3/4 cup cooking liquid, drain the pasta, and return it to the pot.

Meanwhile, grate the zucchini on the large holes of a box grater, turning the zucchini to grate the outside first (discard the soft core). In a large bowl, toss together the tomatoes, olive oil, 2 tablespoons pesto, and 1/4 teaspoon each salt and pepper. Fold in the zucchini and mozzarella.

Toss the pasta with the remaining pesto and 1/4 cup of the reserved pasta water (adding more if the pasta seems dry). Fold in the tomato-zucchini mixture and sprinkle with basil, if desired.

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